ESPN Injury page says Howard's estimated return is July 17th, which is the Dreams last game before the break. She last played on June 16th vs Minnesota.
Olympics start July 26th. I would think if the Olympic team was going to walk in the opening ceremonies they would have to leave the USA on July 24th. First 3 x 3 game is July 30th.
The thing about the 3 x 3 games roster is, you cant go over without healthy players, you only take 4. Extremely hard to play with 3 or 3.5 healthy players. I dont recall if you can bring an extra(doubt it) nor if you can use a 5 x 5 player on your countries team, nor add a player after the games start. The 5 x 5 roster has 12, so if you have a question mark I am sure the team can survive with 11, or even 10 healthy players.